Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def main():
    from bisect import bisect_left
    n = int(input()) * 2
    l = [i * (i + 1) for i in range(1, int(n ** .5) + 2)]
    for a in l:
        b = l[bisect_left(l, n - a)]
        if b <= a or a + b == n:
            break
    print(("NO", "YES")[a + b == n])


if __name__ == '__main__':
    main()